Critical variables are defined, for example in thermodynamics, in terms of the values of variables at the critical point.

On a PV diagram, the critical point is an inflection point. Thus:

$$

\left(\frac{\partial P}{\partial V}\right)_{C}=0

$$

\left(\frac{\partial^2 P}{\partial V^2}\right)_{C}=0

For the van der Waals equation, the above yields:

$$

P_C=\frac{a}{27b^2}

$$

v_C=3b

$$

T_C=\frac{8a}{27bR}

Thermodynamics | Conformal field theory

Variable crítica